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If $\mathbf{a} \neq \mathbf{0}, \mathbf{b} \neq \mathbf{0}, \mathbf{c} \neq 0, \mathbf{a} \times \mathbf{b}=\mathbf{0}$ and $\mathbf{b} \times \mathbf{c}=0$, then $\mathbf{a} \times \mathbf{c}$ is equal to
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The correct answer is:
$0$
Given,
$$
a \neq 0, b \neq 0, c \neq 0 \text { and } a \times b=0, b \times c=0
$$
$\mathbf{a} \times \mathbf{b}=\mathbf{0} \quad \Rightarrow$ Vector $\mathbf{a}$ and $\mathbf{b}$ are parallel.
$\Rightarrow \mathbf{a}$ and $\mathbf{c}$ are also parallel.
$$\Rightarrow a \times c=0$$
$$
a \neq 0, b \neq 0, c \neq 0 \text { and } a \times b=0, b \times c=0
$$
$\mathbf{a} \times \mathbf{b}=\mathbf{0} \quad \Rightarrow$ Vector $\mathbf{a}$ and $\mathbf{b}$ are parallel.
$\Rightarrow \mathbf{a}$ and $\mathbf{c}$ are also parallel.
$$\Rightarrow a \times c=0$$
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